Properties

Label 103488fx
Number of curves $2$
Conductor $103488$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fx1")
 
E.isogeny_class()
 

Elliptic curves in class 103488fx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
103488.cq1 103488fx1 \([0, -1, 0, -1633, 8065]\) \(62500/33\) \(254438080512\) \([2]\) \(92160\) \(0.88008\) \(\Gamma_0(N)\)-optimal
103488.cq2 103488fx2 \([0, -1, 0, 6207, 56673]\) \(1714750/1089\) \(-16792913313792\) \([2]\) \(184320\) \(1.2267\)  

Rank

sage: E.rank()
 

The elliptic curves in class 103488fx have rank \(0\).

Complex multiplication

The elliptic curves in class 103488fx do not have complex multiplication.

Modular form 103488.2.a.fx

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + q^{11} + 2 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.